Warwick Mathematics Institute Events
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Upcoming Seminars

Geometry and Topology on 01 December 2022 at 14:00 in B3.02
Speaker: Koji Fujiwara (Kyoto University)
Title: The rates of growth in a hyperbolic group
Abstract: I discuss the set of rates of growth of a finitely generated group with respect to all its finite generating sets. In a joint work with Sela, for a hyperbolic group, we showed that the set is wellordered, and that each number can be the rate of growth of at most finitely many generating sets up to automorphism of the group. I may discuss its generalization to acylindrically hyperbolic groups.

Probability Seminar on 01 December 2022 at 16:00 in MS.04 and online here
Speaker: Sunil Chhita (University of Durham)
Title: Domino Shuffle and Matrix Refactorizations
Abstract: This talk is motivated by computing correlations for domino tilings of the Aztec diamond. It is inspired by two of the three distinct methods that have recently been used in the simplest case of a doubly periodic weighting, that is the twoperiodic Aztec diamond. This model is of particular probabilistic interest due to being one of the few models having a boundary between polynomially and exponentially decaying macroscopic regions in the limit. One of the methods to compute correlations, powered by the domino shuffle, involves inverting the Kasteleyn matrix giving correlations through the local statistics formula. Another of the methods, driven by a WienerHopf factorization for two bytwo matrix valued functions, involves the EynardMehta theorem. For arbitrary weights the WienerHopf factorization can be replaced by an LU and ULdecomposition, based on a matrix refactorization, for the product of the transition matrices. In this talk, we present results to say that the evolution of the face weights under the domino shuffle and the matrix refactorization is the same. This is based on joint work with Maurice Duits (Royal Institute of Technology KTH).

Applied Mathematics on 02 December 2022 at 12:00 in B3.02
Speaker: Katherine Kamal (Cambridge)
Title: The microhydrodynamics of ultrathin nanoparticles: modelling to predict the "unseen"
Abstract: Graphene nanoparticles are ubiquitous, used in everything from the design of more robust extreme weatherresistance spacecraft to flexibleelectronics tracks. Made from just a few atomic layers, the instantaneous dynamics of these platelike particles in flowing liquids are, experimentally, practically inaccessible. We study theoretically and computationally the microhydrodynamics of dilute suspensions of graphene in a simple viscous shear flow field. In the infinite Péclet number limit, a rigid platelet with the interfacial hydrodynamic slip properties of graphene does not follow the periodic rotations predicted for classical colloidal particles but aligns itself at a slight inclination angle with respect to the flow. This unexpected result is due to the hydrodynamic slip reducing the tangential stress at the grapheneliquid surface. By analysing the FokkerPlank equation for the orientational distribution function for decreasing Péclet numbers, we explore how hydrodynamic slip affects the particle’s orientation and effective viscosity. We find that hydrodynamic slip can dramatically change the average particle’s orientation and effective viscosity. For example, the effective viscosity of a dilute suspension of graphene platelets is predicted to be smaller than the base fluids under certain flow conditions for typical slip length values.

Combinatorics on 02 December 2022 at 14:00 in B3.02
Speaker: Bernd Schulze (University of Lancaster)
Title: Geometric Rigidity Theory and Applications
Abstract: In the last two decades or so the subject has become particularly active, drawing on diverse areas of mathematics, and engaging with a growing range of modern applications, such as Engineering, Robotics, ComputerAidedDesign, Molecular Dynamics, and Materials Science.
In the first part of the talk, I will give an introduction to Geometric Rigidity Theory, concentrating on some key combinatorial results and problems for barjoint frameworks, but also describing how these have been extended to some other types of frameworks.
Since many realworld structures are symmetric, a major recent research direction in the field is to study the impact of symmetry on the rigidity and flexibility of barjoint frameworks. I will show how group representation theory can be used to reveal `hidden' infinitesimal motions and states of selfstress in symmetric frameworks that cannot be detected with the standard nonsymmetric counts. Finally, I will show how these symmetrybased methods can be used as a design tool for gridshell structures. This is recent joint work with William Baker, Arek Mazurek and Cameron Millar. 
Colloquium on 02 December 2022 at 16:00 in B3.02
Speaker: Tara Brendle (Glasgow)
Title: Twists and trivializations: encoding symmetries of manifolds
Abstract: The classification of 2manifolds in the first half of the 20th century was a landmark achievement in mathematics, as was the more recent (and more complicated) classification of 3manifolds completed by Perelman. The story does not end with classification, however: there is a rich theory of symmetries of manifolds, encoded in their mapping class groups. In this talk we will explore some aspects of mapping class groups in dimensions 2 and 3, with a focus on illustrative examples.

Number Theory on 05 December 2022 at 15:00 in B3.02
Speaker: Istvan Kolossvary (St Andrews)
Title: Distance between natural numbers based on their prime signature
Abstract: One can define different metrics between natural numbers based on their unique prime signature. Fixing such a metric, we are interested in the asymptotic growth rate of the arithmetic function L(N) which tabulates the cumulative sum of distances between consecutive natural numbers up to N. In particular, choosing the maximum norm, we will show that the limit of L(N)/N exists and is equal to the expected value of a certain random variable. We also demonstrate that prime gaps exhibit a richer structure than on the traditional number line and pose a number of problems. Joint work with Istvan B. Kolossvary.

Algebra on 05 December 2022 at 17:00 in B3.02
Speaker: Ana Retegan (University of Birmingham)
Title: TBC
Abstract: TBC

Partial Differential Equations and their Applications on 06 December 2022 at 12:00 in B3.02
Speaker: Antonio Esposito (University of Oxford)
Title: TBA
Abstract: TBA

Geometry and Topology on 08 December 2022 at 14:00 in B3.02
Speaker: Ric Wade (University of Oxford)
Title: Autinvariant quasimorphisms on groups
Abstract: For a large class of groups, we exhibit an infinitedimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includes nonelementary hyperbolic groups, infinitelyended finitely generated groups, some relatively hyperbolic groups, and a class of graph products of groups that includes all rightangled Artin and Coxeter groups that are not virtually abelian. Joint work with Francesco FournierFacio.

Combinatorics on 09 December 2022 at 14:00 in B3.02
Speaker: Zoltán Vidnyánszky (Eötvös Loránd University)
Title: Borel combinatorics, the LOCAL model and complexity
Abstract: In the first part of the talk, I will give an overview of the field of Borel combinatorics and its recently uncovered connections to the LOCAL model of distributed computing. Then, I will discuss complexity related aspects of the field. Namely, I will consider the question of how hard it is to decide the existence of Borel homomorphisms from a Borel structure to a given finite structure.

Colloquium on 09 December 2022 at 16:00 in B3.02
Speaker: John Baez (UC Riverside)
Title: Category Theory in Epidemiology
Abstract: Category theory provides a general framework for building models of dynamical systems. We explain this framework and illustrate it with the example of "stock and flow diagrams". These diagrams are widely used for simulations in epidemiology. Although tools already exist for drawing these diagrams and solving the systems of differential equations they describe, we have created a new software package called StockFlow which uses ideas from category theory to overcome some limitations of existing software. We illustrate this with code in StockFlow that implements a simplified version of a COVID19 model used in Canada. This is joint work with Xiaoyan Li, Sophie Libkind, Nathaniel Osgood and Evan Patterson.

Algebraic Geometry on 30 November 2022 at 15:00
Speaker: Cancelled (n/a)
Title: n/a
Abstract: n/a

Postgraduate on 30 November 2022 at 12:00
Speaker: Nuno Arala Santos (University of Warwick)
Title: Counting Rational Points on Cubic Surfaces
Abstract: A fundamental problem in Diophantine geometry is to understand the asymptotic behaviour of the number of solutions to a Diophantine equation when we impose a boundedness condition on the variables. We will explain some progress in this problem for equations defining cubic surfaces in 3dimensional space, following Roger HeathBrown.

Algebraic Topology on 29 November 2022 at 16:00
Speaker: Florian Naef (Trinity College Dublin)
Title: Relative intersection product, Whiteheadtorsion and string topology
Abstract: Given a closed oriented manifold one can define an intersection product on the homology. This can be extended to local coefficient, and further made relative to the diagonal. I will explain how such a relative selfintersection product is not homotopy invariant (in contrast to the ordinary intersection product) and how this is picked up by string topology. Eventually, we will identify the error term with the trace of Whitehead torsion. More precisely, we will extract an invariant from a Poincare embedding of the diagonal (in the sense of J. Klein) that is the trace of (a version of) Reidemeister torsion. This is based on joint work with P. Safronov.

Algebra on 28 November 2022 at 17:00
Speaker: Rachel Pengelly (University of Birmingham)
Title: TBC
Abstract: TBC

Number Theory on 28 November 2022 at 15:00
Speaker: Alexandre Maksoud (Paderborn)
Title: The arithmetic of the adjoint of a weight 1 modular form
Abstract: A conjecture of Darmon, Lauder and Rotger expresses padic iterated integrals attached to a pair of weight 1 modular forms (f,g) in terms of padic logarithms of certain units attached to f and g. This talk reports a work in progress in which we explain, in the case where f=g, how to interpret this conjecture as a variant of the GrossStark conjecture for the adjoint of f. This requires studying the specializations of the congruence module attached to a Hida deformation of f.

Colloquium on 25 November 2022 at 16:00
Speaker: Cancelled ()
Title: 
Abstract: 

Applied Mathematics on 25 November 2022 at 12:00
Speaker: Eric Neiva (Collége de France & CNRS)
Title: Unfitted finite element methods: decoupling the mesh from the geometry
Abstract: The finite element method (FEM) approximates a PDE from a variational formulation of the problem. Its standard formulation requires a mesh fitting to the boundary of the geometry of interest. Yet, for many problems of practical interest, the geometry is so intricate that mesh generation requires frequent and timeconsuming manual intervention. Boundaryfitted meshing can be avoided with unfitted or immersed FEMs. The main idea is to embed the geometry in a simple mesh (e.g., a Cartesian grid) and define the discretisation in the cells intersecting the geometry. In this talk, we will describe a novel unfitted FEM that circumvents the classical issue of immersed FEM: illconditioning due small celltogeometry intersections We will discuss its application to early embryo development in animals.

Junior Analysis and Probability Seminar on 24 November 2022 at 13:00
Speaker: Giacomo del Nin (University of Warwick)
Title: Isoperimetric shapes in Penrose tilings
Abstract: TBA

Probability Seminar on 23 November 2022 at 16:00
Speaker: PierreFrancois Rodriguez (Imperial College London)
Title: Scaling in lowdimensional longrange percolation models
Abstract: The talk will present recent progress towards understanding the critical behavior of dimensional percolation models exhibiting longrange correlations. The results rigorously exhibit the scaling behavior of various observables of interest and are consistent with scaling theory below the uppercritical dimension (expectedly equal to 6).

Algebraic Geometry on 23 November 2022 at 15:00
Speaker: Jonathan Lai (Imperial)
Title: A Reconciliation of Mutations and Potentials
Abstract: Given a lattice polygon, one can consider the spanning fan to obtain a toric variety. A combinatorial mutation is an operation that takes one polygon to another, which induces a degeneration of one toric variety to the other. One can then attempt to study all toric degenerations of a fixed Fano variety through the study of polygons and their mutations. In another world, a set of algebraic tori can be glued together by birational maps, also called mutations, to form a cluster variety.
In this talk, I will explain a justification coming from mirror symmetry on why these two operations deserve to share the same name (in dimension 2). Given an orbifold del Pezzo surface X, there is a natural cluster variety Y that knows about the polytopes and mutations associated to X. Namely, there is a combinatorial object associated to Y called a scattering diagram, which is a collection of walls inside a vector space. The chambers, which correspond to tori in Y, are precisely the polygons coming from toric degenerations of X. This is based off ongoing joint work with Tim Magee and Ben Wormleighton. 
Postgraduate on 23 November 2022 at 12:00
Speaker: Alexandros Groutides (University of Warwick)
Title: Galois representations attached to elliptic curves and the Open Image Theorem
Abstract: A Galois representation is a homomorphism $\rho:Gal(\bar{K}/K)\longrightarrow Aut(V)$ where $V$ is a finite dimensional vector space or a free module of finite rank. These objects are of great importance in number theory due to their connections with elliptic curves, modular forms and $L$functions. We will introduce the mod$\ell$, $\ell$adic and adelic Galois representations attached to a nonCM elliptic curve and discuss the structure of their image. The $\ell$adic open image does not a priori imply the adelic open image but as we will see, it all boils down to the surjectivity of the more innocent sounding mod$\ell$ representation.

Algebraic Topology on 22 November 2022 at 16:00
Speaker: Irakli Patchkoria (University of Aberdeen)
Title: Morava Ktheory of infinite groups and Euler characteristic
Abstract: Given an infinite discrete group G with a finite model for the classifying space for proper actions, one can define the Euler characteristic of G and the orbifold Euler characteristic of G. In this talk we will discuss higher chromatic analogues of these invariants in the sense of stable homotopy theory. We will study the Morava Ktheory of G and associated Euler characteristic, and give a character formula for the LubinTate theory of G. This will generalise the results of HopkinsKuhnRavenel from finite to infinite groups and the Ktheoretic results of Adem, Lück and Oliver from chromatic level one to higher chromatic levels. Along the way we will give explicit computations for amalgamated products of finite groups, right angled Coxeter groups and certain special linear groups. This is all joint with Wolfgang Lück and Stefan Schwede.

Ergodic Theory and Dynamical Systems on 22 November 2022 at 15:30
Speaker: Tim Austin (UCLA)
Title: Positive sofic entropy without relatively Bernoulli factors.
Abstract: The classical Kolmogorov–Sinai entropy is an invariant of probabilitypreserving transformations. Much of the resulting theory was successfully extended to actions of discrete amenable groups by Ornstein, Weiss and others.
Lewis Bowen’s more recent notion of sofic entropy extends the Kolmogorov–Sinai definition to actions of sofic groups, a much larger class introduced by Gromov. A range of natural questions concern how entropy and its consequences differ between the sofic setting the amenable one.
After reviewing a special case of sofic entropy for certain freeproduct groups, this talk will present a new example of an action of such a group. The example has positive sofic entropy, but has no splitting as a direct product involving a Bernoulli factor. This contrasts with the world of amenable group actions, where many such splittings are guaranteed by the weak Pinsker theorem. The new example is an algebraic action, and its analysis depends on (slight modifications of) results
from the theory of random regular lowdensity paritycheck codes.
This material is part of an ongoing joint project with Lewis Bowen, Brandon Seward and Christopher Shriver.
(This talk will be a continuation of the colloquium from Friday Nov 18th, and will assume some of the notions from that talk.) 
Ergodic Theory and Dynamical Systems on 22 November 2022 at 14:00
Speaker: Timothée Bénard (Cambridge)
Title: The local limit theorem for biased random walks on nilpotent groups
Abstract: We prove the local limit theorem for biased random walks on a simply connected nilpotent Lie group G. The result allows to approximate at scale 1 the nstep distribution of a walk by the time n of a smooth diffusion process for a new group structure on G. We also show this approximation is robust under deviation. The proof uses a Gaussian replacement scheme, combining Fourier analysis and a swapping argument inspired by the work of DiaconisHough. As a consequence, we obtain a probabilistic version of Ratner's theorem: Adunipotent random walks on finitevolume homogeneous spaces equidistribute toward algebraic measures.

Partial Differential Equations and their Applications on 22 November 2022 at 12:00
Speaker: Annika Bach (Sapienza Università di Roma)
Title: TBA
Abstract: TBA

Algebra on 21 November 2022 at 17:00
Speaker: Diego Martin Duro (University of Warwick)
Title: TBC
Abstract: TBC

Number Theory on 21 November 2022 at 15:00
Speaker: Rachel Greenfeld (IAS)
Title: Aperiodicity of translational tilings
Abstract: Translational tiling is a covering of a space using translated copies of some building blocks, called the "tiles", without any positive measure overlaps. What are the possible ways that a space can be tiled?
A well known conjecture in this area is the periodic tiling conjecture, which asserts that any tile of Euclidean space admits a periodic tiling. In a joint work with Terence Tao, we construct a counterexample to this conjecture. In the talk, I will survey the study of the periodicity of tilings and discuss our recent progress. 
Colloquium on 18 November 2022 at 16:00
Speaker: Tim Austin (UCLA)
Title: Some recent developments around entropy in ergodic theory
Abstract: The entropy rate of a stationary sequence of random symbols was introduced by Shannon in his foundational work on information theory in 1948. In the early 1950s, Kolmogorov and Sinai realized that they could turn this quantity into an isomorphism invariant for measurepreserving transformations on a probability space. Almost immediately, they used it to distinguish many examples called "Bernoulli shifts" up to isomorphism. This resolved a famous open question of the time, and ushered in a new era for ergodic theory.
In the decades since, entropy has become one of the central concerns of ergodic theory, having widespread consequences both for the abstract structure of measurepreserving transformations and for their behaviour in applications. In this talk, I will review some of the highlights of the structural story, and then discuss Bowen's more recent notion of `sofic entropy'. This generalizes KolmogorovSinai entropy to measurepreserving actions of many `large' nonamenable groups including free groups. I will end with a recent result illustrating how the theory of sofic entropy has some striking differences from its older counterpart.
This talk will be aimed at a general mathematical audience. Most of it should be accessible given a basic knowledge of measure theory, probability, and a little abstract algebra. 
Combinatorics on 18 November 2022 at 14:00
Speaker: Shoham Letzter (UCL)
Title: Separating paths systems of almost linear size
Abstract: A separating path system for a graph G is a collection P of paths in G such that for every two edges e and f, there is a path in P that contains e but not f. We show that every nvertex graph has a separating path system of size O(n log* n). This improves upon the previous best upper bound of O(n log n), and makes progress towards a conjecture of FalgasRavry–Kittipassorn–Korándi–Letzter–Narayanan and Balogh–Csaba–Martin–Pluhár, according to which an O(n) bound should hold.

Applied Mathematics on 18 November 2022 at 12:00
Speaker: Anna Song (Imperial)
Title: Describing tubular shapes and branching membranes with geometry and topology
Abstract: Tubular and membranous shapes are important mathematical structures that arise in many biomedical applications. Morphology is linked to function: their branching patterns, shaped by interactions and remodelled by diseases, inform us on a biological system.
I will present the “curvatubes” model, which unifies a wide continuum of porous shapes within a common geometric framework (https://doi.org/10.1007/s10851021010499). It generalizes the Helfrich model for biomembranes by considering shapes as optimizers of a curvature functional in which the principal curvatures may play asymmetric roles. The geometric problem is approximated by a novel phasefield formulation that satisfies a Gammalimsup property, and is readily implementable as a GPU algorithm. The framework is very flexible and shape textures can be aligned, spatialized, or constrained on a domain.
In the remaining time, I will introduce some topological approaches to analyze such structures using persistent homology, and how they may empirically quantify the "texture of shapes". These are tested on proprietary images of bone marrow vasculature remodelled in acute myeloid leukaemia.
Overall, these compact descriptions offer a unified view to branching tubules and membranes, and will potentially lead to applications in bioengineering, imaging, or materials science. 
Geometry and Topology on 17 November 2022 at 14:00
Speaker: Bradley Zykoski (Univeristy of Michigan)
Title: A polytopal decomposition of strata of translation surfaces
Abstract: A closed surface can be endowed with a certain locally Euclidean metric structure called a translation surface. Moduli spaces that parametrize such structures are called strata. There is a GL(2,R)action on strata, and orbit closures of this action are rare gems, the classification of which has been given a huge boost in the past decade by landmark results such as the "Magic Wand" theorem of EskinMirzakhaniMohammadi and the Cylinder Deformation theorem of Wright. Investigation of the topology of strata is still in its nascency, although recent work of CalderonSalter and CostantiniMöllerZachhuber indicate that this field is rapidly blossoming. In this talk, I will discuss a way of decomposing strata into finitely many higherdimensional polytopes. I will discuss how I have used this decomposition to study the topology of strata, and my ongoing work using this decomposition to study the orbit closures of the GL(2,R)action.

Junior Analysis and Probability Seminar on 17 November 2022 at 13:00
Speaker: Jakub Takác (University of Warwick)
Title: Norms in finite dimensions and rectifiability in metric spaces
Abstract: TBA

Probability Seminar on 16 November 2022 at 16:00
Speaker: Sam OleskerTaylor (University of Warwick)
Title: Random Walks on Random Cayley GraphsTBA
Abstract: TBAhttps://teams.microsoft.com/l/meetupjoin/19%3ameeting_Mjg1MDU2MDQtY2NlZS00Y2NlLWFhNWUtZWRiMmEwYjI0ZGEz%40thread.v2/0?context=%7b%22Tid%22%3a%2209bacfbd47ef446592653546f2eaf6bc%22%2c%22Oid%22%3a%22325bf9e5c56a4d319811aa22fe105e13%22%7d
Join conversation
teams.microsoft.com
We investigate mixing properties of RWs on random Cayley graphs of a finite group G with
k≫ 1 independent, uniformly random generators, with 1 ≪ log k ≪ log G.
Aldous and Diaconis (1985) conjectured that the RW on this random graph exhibits cutoff for any group G whenever k ≫ log G and further that the cutoff time depends only on k and G. It was established for Abelian groups.
We disprove the second part of the conjecture by considering RWs on uppertriangular matrices. We extend this conjecture to 1 ≪ k ≲ log G, verifying a version of it for arbitrary Abelian groups under 'almost necessary' conditions on k.
It is all joint work with Jonathan Hermon (now at UBC). 
Algebraic Geometry on 16 November 2022 at 15:00
Speaker: Ruijie Yang (HumboldtUniversität zu Berlin)
Title: Zeroes of one forms and homologically trivial deformations
Abstract: In 1926, Hopf proved the PoincaréHopf theorem, which implies that if a compact differential manifold admits a nowhere vanishing vector field, then its topological Euler characteristic is zero. Dually, it is natural to ask the same question for one forms. In 1970, Tischler proved that the existence of a nowhere vanishing real closed one form induces a differentiable fiber bundle structure over the circle. In 2013, Kotschick conjectured that for compact Kähler manifolds, admitting a nowhere vanishing real closed one form is actually equivalent to the existence of a nowhere vanishing holomorphic one form. In this talk, I will show that Kotschick’s conjecture can be deduced from a conjecture of BobadillaKollár on homologically trivial deformation. Therefore, Kotschick’s conjecture is true if the first Betti number of X is at least 2dim(X)2 and the Albanese variety of X is simple. This is joint work with Stefan Schreieder.

Postgraduate on 16 November 2022 at 12:00
Speaker: Andrew Ronan (University of Warwick)
Title: Exact couples and nilpotent spaces
Abstract: We will introduce spectral sequences via exact couples and outline how to derive the Serre spectral sequence from algebraic topology. Then, we will introduce nilpotent spaces, which are a type of space in many ways dual to a CW complex, before explaining how the Serre spectral sequence can be used to derive some of their properties. For example, the homology groups of a nilpotent space are finitely generated if and only if its homotopy groups are finitely generated.

Algebraic Topology on 15 November 2022 at 16:00
Speaker: Foling Zou (University of Michigan)
Title: Nonabelian Poincare duality theorem in equivariant factorization homology
Abstract: The factorization homology are invariants of ndimensional manifolds with some fixed tangential structures that take coefficients in suitable Enalgebras. In this talk, I will give a definition for the equivariant factorization homology of a framed manifold for a finite group G by monadic bar construction following KupersMiller. Then I will prove the equivariant nonabelian Poincare duality theorem in this case. As an application, in joint work with Asaf Horev and Inbar Klang, we compute the equivariant factorization homology on equivariant spheres for certain Thom spectra. In particular, we recover a computation of the Real topological Hoschild homology by DottoMoiPatchkoriaReeh.

Ergodic Theory and Dynamical Systems on 15 November 2022 at 14:00
Speaker: Mar Giralt (Universitat Politecnica de Catalunya)
Title: Chaotic dynamics, exponentially small phenomena and Celestial Mechanics
Abstract: A fundamental problem in dynamical systems is to prove that a given model has chaotic dynamics. One of the methods employed to prove this type of motions is to verify the existence of transversal intersections between the stable and unstable manifolds of certain objects. Then, there exists a theorem (the SmaleBirkhoff homoclinic theorem) which ensures the existence of chaotic motions. In this talk we present a method to analyze the distance and transversality between certain stable and unstable manifolds when a small perturbation is added to an integrable system. In particular, we consider the case where the distance between manifolds is exponentially small. This implies that this difference cannot be detected by expanding the manifolds into a series with respect to the small perturbation parameter. Therefore, classical perturbation theory cannot be applied. Finally, we apply these techniques to a celestial mechanics problem. In particular, we study the Lagrange point L_3 in the restricted planar circular 3body problem.

Algebra on 14 November 2022 at 17:00
Speaker: Jay Taylor (University of Manchester)
Title: TBC
Abstract: TBC

Number Theory on 14 November 2022 at 15:00
Speaker: Rosa Winter (KCL)
Title: Density of rational points on del Pezzo surfaces of degree 1
Abstract: Let X be an algebraic variety over an infinite field k. In arithmetic geometry we are interested in the set X(k) of krational points on X. For example, is X(k) empty or not? And if it is not empty, is X(k) dense in X with respect to the Zariski topology?
Del Pezzo surfaces are surfaces classified by their degree d, which is an integer between 1 and 9 (for d >= 3, these are the smooth surfaces of degree d in P^d). For del Pezzo surfaces of degree at least 2 over a field k, we know that the set of krational points is Zariski dense provided that the surface has one krational point to start with (that lies outside a specific subset of the surface for degree 2). However, for del Pezzo surfaces of degree 1 over a field k, even though we know that they always contain at least one krational point, we do not know if the set of krational points is Zariski dense in general.
I will talk about density of rational points on del Pezzo surfaces, state what is known so far, and show a result that is joint work with Julie Desjardins, in which we give sufficient and necessary conditions for the set of krational points on a specific family of del Pezzo surfaces of degree 1 to be Zariski dense, where k is finitely generated over Q. 
Colloquium on 11 November 2022 at 16:00
Speaker: Yan Fyodorov (King's College London)
Title: "Escaping the crowds": extreme values and outliers in rank1 nonnormal deformations of GUE/CUE
Abstract: Rank1 nonnormal deformations of GUE/CUE provide the simplest model for describing resonances in a quantum chaotic system decaying via a single open channel. In the case of GUE we provide a detailed description of an abrupt restructuring of the resonance density in the complex plane as the function of channel coupling, identify the critical scaling of typical extreme values, and finally describe how an atypically broad resonance (an outlier) emerges from the crowd. In the case of CUE we are further able to study the Extreme Value Statistics of the ''widest resonances'' and find that in the critical regime it is described by a distribution nontrivially interpolating between Gumbel and Frechet. The presentation will be based on the joint works with Boris Khoruzhenko and Mihail Poplavskyi.

Combinatorics on 11 November 2022 at 14:00
Speaker: Adva Mond (University of Cambridge)
Title: Minimum degree edgedisjoint Hamilton cycles in random directed graphs
Abstract: At most how many edgedisjoint Hamilton cycles does a given directed graph contain? A trivial upper bound is the minimum between the minimum out and indegrees. We show that a typical random directed graph D(n,p) contains precisely this many edgedisjoint Hamilton cycles, given that p >= (log^3 n)/n, which is optimal up to a factor of log^

Applied Mathematics on 11 November 2022 at 12:00
Speaker: Fabian Spill  POSTPONED TO TERM 2 (Birmingham)
Title: Mechanics, Geometry and Topology of Health and Disease
Abstract: TBAExperimental biologists traditionally study biological functions as well as diseases mostly through their abnormal molecular or cellular features. For example, they investigate genetic abnormalities in cancer, hormonal imbalances in diabetes, or an aberrant immune system in vascular diseases. However, many diseases also have a mechanical component which is critical to their deadliness. Notably, cancer kills mostly through metastasis, where the cancer cells acquire the capability to change their physical attachments and migrate. Such mechanical alterations also change geometrical features, such as the cell shape, or topological features, such as the organisation of vascular networks and cellular neighbourhoods within a tissue.
While some of these mechanical, geometrical or topological features in biology are long known, the traditional perspective is to consider them as emergent from molecular features. However, mechanical, geometrical and topological features can also affect the molecular state of a cell. Therefore, the most complete view of many biological systems is to consider them as a complex mechanochemical systems. Diseases such as cancer are then interpreted as perturbations to this system that cannot be solely explained by considering one feature in isolation (such as a single mutation that ‘causes’ cancer).
I will discuss several examples of systems where this mechanical/geometrical/topological coupling to molecular features plays a crucial role: cells that change their shape, blood vessel cells that open gaps to let cancer cells pass during metastasis, and mitochondria that change their organisation in diabetes. 
Mathematics Teaching and Learning on 10 November 2022 at 16:00
Speaker: Edmund Robertson (St. Andrews)
Title: MacTutor – a collection of great mathematicians?
Abstract: In my talk I will look at questions such as: Is MacTutor a collection of great mathematicians? What is a “great mathematician?” How did I choose whom to write about?

Junior Analysis and Probability Seminar on 10 November 2022 at 13:00
Speaker: Simon Gabriel (University of Warwick)
Title: On the Poisson–Dirichlet diffusion and Trotter–Kurtz approximations
Abstract: TBA

Probability Seminar on 09 November 2022 at 16:00
Speaker: Kevin Yang (UC Berkeley)
Title: Timedependent KPZ equation from nonequilibrium GinzburgLandau SDEs
Abstract: This talk has two goals. The first is the derivation of a timedependent KPZ equation (TDKPZ) from a timeinhomogeneous GinzburgLandau model. To our knowledge, said TDKPZ has not yet been derived from microscopic considerations. It has a nonlinear twist that is not seen in the usual KPZ equation, making it a more interesting SPDE.
The second goal is the universality of the method (for deriving TDKPZ), which should work beyond GinzburgLandau. In particular, we answer a question of deriving (TD)KPZ from asymmetric particle systems under natural fluctuationscale versions of the assumptions in Yau’s relative entropy method and a logSobolev inequality. This gives some progress on open questions posed at a workshop on KPZ at the American Institute of Math. Time permitting, future directions (of both pure and applied mathematical flavors) will be discussed. 
Algebraic Geometry on 09 November 2022 at 15:00
Speaker: Beihui Yuan (Swansea)
Title: 16 Betti diagrams of Gorenstein CalabiYau varieties and a Betti stratification of Quaternary Quartic Forms
Abstract: Motivated by the question of finding all possible projectively normal CalabiYau 3folds in 7dimensional projective spaces, we proved that there are 16 possible Betti diagrams for arithmetically Gorenstein ideals with regularity 4 and codimension 4. Among them, 8 Betti diagrams have been identified with those of CalabiYau 3folds appeared in a list of 11 families founded by CoughlanGolebiowskiKapustkaKapustka. Another 8 cannot be Betti diagrams of any smooth irreducible nondegenerate 3fold. Based on the apolarity correspondence between Gorenstein ideals and homogeneous polynomials, and on our results on 16 Betti diagrams, we describe a stratification of the space of quartic forms in four variables.
This talk is based on the paper “CalabiYau threefolds in P^n and Gorenstein rings” by Hal Schenck, Mike Stillman and Beihui Yuan, and the preprint “Quaternary quartic forms and Gorenstein rings” by Michal and Grzegorz Kapustka, Kristian Ranestad, Hal Schenck, Mike Stillman and Beihui Yuan. 
Algebraic Topology on 08 November 2022 at 16:00
Speaker: Thibault Décoppet (Oxford)
Title: Fusion 2Categories associated to 2groups
Abstract: Motivated by the cobordism hypothesis, which provides a correspondence between fully dualizable objects and fully extended framed TQFTs, it is natural to seek out interesting examples of fully dualizable objects. In dimension four, the fusion 2categories associated to 2groups are examples of fully dualizable objects. In my talk, I will begin by reviewing the 2categorical notion of Cauchy completion, and recall the definition of a fusion 2category in detail. Then, I will explain how one can construct a fusion 2category of 2vector spaces graded by 2group, and how this construction can be twisted using a 4cocycle. Finally, it is important to understand when two such fusion 2categories yield equivalent TQFTs. The answer is provided by the notion of Morita equivalence between fusion 2categories, which will be illustrated using some examples.

Number Theory on 08 November 2022 at 15:00
Speaker: George Boxer (Imperial)
Title: Higher Hida theory for Siegel modular varieties
Abstract: The goal of higher Hida theory is to study the ordinary part of coherent cohomology of Shimura varieties integrally. We introduce a higher coherent cohomological analog of Hida's space of ordinary padic modular forms, which is defined as the ordinary part of the coherent cohomology with "partial compact support" of the ordinary Igusa variety. Then we give an analog of Hida's classicality theorem in this setting. This is joint work with Vincent Pilloni.

Ergodic Theory and Dynamical Systems on 08 November 2022 at 14:00
Speaker: Donald Robertson (University of Manchester)
Title: Dynamical Cubes and Ergodic Theory
Abstract: n recent works Kra, Moreira, Richter and I showed that positive density sets always contain sums of any finite number of infinite sets, and a shift of the selfsum of an infinite set. The main step in our approach was to prove the existence of certain dynamical configurations described via limit points of orbits. In this talk I will describe what these configurations are, and explain how ergodic theory can be used to deduce their existence.

Partial Differential Equations and their Applications on 08 November 2022 at 12:00
Speaker: Angeliki Menegaki (IHES)
Title: TBA
Abstract: TBA

Algebra on 07 November 2022 at 17:00
Speaker: Michael Bate (University of York)
Title: TBC
Abstract: TBC

Colloquium on 04 November 2022 at 16:00
Speaker: Giovanni Alberti (Pisa)
Title: Small sets in Geometric Measure Theory and Analysis
Abstract: Many relevant problems in Geometric Measure Theory can be ultimately understood in terms of the structure of certain classes of sets, which can be loosely described as "small" (in some sense or another). In this talk I will review a few of these problems and related results, and highlight the connections to other areas of Analysis.

Combinatorics on 04 November 2022 at 14:00
Speaker: Alp Müyesser (UCL)
Title: Hypergraphs defined by groups
Abstract: This talk will be about a genre of problems where one looks for spanning structures in hypergraphs where vertices represent group elements, and edges represent solutions to systems of equations. Problems expressible using this framework include the HallPaige conjecture, the nqueens problem, the harmonious labelling conjecture, Snevily's subsquare conjecture, and many others. We will discuss an absorptionbased attack on problems of this type which has resolved many longstanding conjectures in the area.
Joint work with Alexey Pokrovskiy. 
Applied Mathematics on 04 November 2022 at 12:30
Speaker: Emma Davis (Warwick)
Title: Using compartmental ODE models to forecast the elimination of macroparasitic diseases
Abstract: Standard compartmental models of infectious disease transmission work by categorising a population by stage of infection and then building a system of differential equations that govern the density or number of individuals in each category, e.g. the SIR model has compartments for susceptible (S), infectious (I) and recovered/removed (R) individuals. This makes sense when we are interested in the number of individuals infected over an epidemic where infection is a binary state, as measured by prevalence and incidence, but is less useful for macroparasitic diseases, where infection is instead classified by the number of macroparasites inhabiting any given individual. Models for macroparasitic diseases therefore more commonly consider the number of parasites per individual (their parasite “burden”) or, on a population scale, the mean parasite burden. Common biological features of macroparasitic diseases, such as sexual reproduction of the parasites or indirect transmission routes, and aggregation between individuals, can result in interesting dynamics at low prevalence, which I will discuss using the example of the macroparasitic disease lymphatic filariasis.

Applied Mathematics on 04 November 2022 at 12:00
Speaker: Christian VaqueroStainer (Warwick)
Title: The sedimentation dynamics of thin, rigid disks
Abstract: Sedimentation problems arise in a wide range of natural and industrial processes and exhibit a rich array of phenomenology. A particular motivation for this study is the size segregation of graphene flakes, for which a dominant method is centrifugation in a viscous fluid (Khan 2012). We present a numerical investigation of the sedimentation dynamics of thin, deformed circular disks sedimenting freely under gravity in an otherwise quiescent, Stokesian fluid. In the first part of this study, we address singularities which arise in the fluid pressure and velocity gradient at the edge of the disk, by developing an augmented finite element method to capture the singularities with analytic functions. In the second part of the study, we deploy this method in a fluidstructure interaction framework to examine the behaviour of two distinct classes of disk shape, namely cylindrically and conicallydeformed disks with one and two planes of symmetry, respectively. We explore the geometrydriven dynamics and the bifurcation structure which arises for the conicallydeformed disk as the level of asymmetry is varied.

Geometry and Topology on 03 November 2022 at 14:00
Speaker: Becca Winarski (College of the Holy Cross)
Title: Polynomials, branched covers, and trees
Abstract: Thurston proved that a postcritically finite branched cover of the plane is either equivalent to a polynomial (that is: conjugate via a mapping class) or it has a topological obstruction. We use topological techniques – adapting tools used to study mapping class groups – to produce an algorithm that determines when a branched cover is equivalent to a polynomial, and if it is, determines which polynomial a topological branched cover is equivalent to. This is joint work with Jim Belk, Justin Lanier, and Dan Margalit.

Probability Seminar on 02 November 2022 at 16:00
Speaker: Alessandra Cipriani (University College London)
Title: Properties of the gradient squared of the Gaussian free field
Abstract: TBA

Algebraic Geometry on 02 November 2022 at 15:00
Speaker: Michel van Garrel (Birmingham)
Title: Log Mirror Symmetry
Abstract: Start with a smooth Fano variety X and a smooth anticanonical divisor D. Consider the problem of counting maps from the projective line to X that meet D along a curve in only one point. While this problem is intractable directly, in this joint work with Helge Ruddat and Bernd Siebert, we use toric dualities to translate the problem into a dual problem in a dual geometry. There the problem turns into a problem of computing period integrals, which we can readily solved via the techniques of PicardFuchs equations.
In my talk, I will limit to the case of X the projective plane and D a smooth conic. The beforementioned toric dualities are the constructions of the GrossSiebert programme. I hope to convey the observation that the dualities are natural and that the translation from counting problem to period integral is as well. 
Ergodic Theory and Dynamical Systems on 01 November 2022 at 14:00
Speaker: Carlos Matheus (Ecole Polytechnique)
Title: Elliptic dynamics on certain SU(2) and SU(3) character varieties
Abstract: In this talk, we discuss the action of a hyperbolic element of SL(2,Z) on the SU(2) and SU(3) character varieties of oncepunctured torii. This is based on a joint work with G. Forni, W. Goldman and S. Lawton.

Algebra on 31 October 2022 at 17:00
Speaker: Sean Eberhard (University of Cambridge)
Title: The BostonShalev conjecture for conjugacy classes
Abstract: The BostonShalev conjecture (proved by Fulman and Guralnick in 2015) asserts that in any nonabelian simple group G in any nontrivial permutation action the proportion of derangements is at least some absolute constant c > 0. Since the set of derangements is closed under conjugacy it is also natural to ask about the proportion of *conjugacy classes* containing derangements. It is easy to see that this version of the question has a negative answer for alternating groups, but Guralnick and Zalesski asked whether it holds for groups of Lie type. I will outline a proof. We can also (1) extend to the case of almost simple groups, which is not true for the original conjecture, and (2) deduce the original conjecture, which amounts to a simplification of the FulmanGuralnick proof. The key turns out to be a kind of analytic number theory for palindromic polynomials. This is ongoing work with Daniele Garzoni.

Number Theory on 31 October 2022 at 15:00
Speaker: Yoav Gath (Cambridge)
Title: Lattice point statistics for Cygan–Koranyi balls
Abstract: Euclidean lattice point counting problems, the classical example of which is the Gauss circle problem, are an important topic in classical analysis and have been the driving force behind much of the developments in the area of analytic number theory in the 20th century. In this talk, I will introduce the lattice point counting problem for (2q+1)dimensional Cygan–Koranyi balls, namely, the problem of establishing error estimates for the number of integer lattice points lying inside Heisenberg dilates of the unit ball with respect to the Cygan–Koranyi norm. I will explain how this problem arises naturally in the context of the Heisenberg groups, and how it relates to the Euclidean case (and in particular to the Gauss circle problem). I will survey some of the major results obtained to date for this lattice point counting problem, and in particular, results related to the fluctuating nature of the error term.

Colloquium on 28 October 2022 at 16:00
Speaker: Tom Gur (Warwick Computer Science)
Title: Quantum algorithms and additive combinatorics
Abstract: I will discuss a new connection between quantum computing and additive combinatorics, which allows for boosting the power of quantum algorithms. Namely, I will show a framework that uses generalisations of Bogolyubov’s lemma and Sander’s quasipolynomial BogolyubovRuzsa lemma to transform quantum algorithms that are only correct on a small number of inputs into quantum algorithms that are correct on all inputs.

Applied Mathematics on 28 October 2022 at 12:00
Speaker: Maciej Buze (Birmingham)
Title: Mathematical analysis of atomistic fracture and related phenomena in crystalline materials
Abstract: The modelling of atomistic fracture and related phenomena in crystalline materials poses a string of mathematically nontrivial and exciting challenges, both on the theoretical and practical level. At the heart of the problem lies a discrete domain of atoms (a lattice), which exhibits spatial inhomogeneity induced by the crack surface, particularly pronounced in the vicinity of the crack tip. Atoms interact in a highly nonlinear way, resulting in a severely nonconvex energy landscape facilitating nontrivial behaviour of atoms such as (i) crack propagation; (ii) nearcrack tip plasticity  emission and movement of defects known as dislocations in the vicinity of the crack tip; (iii) surface effects  atoms at the crack surface relaxing or possibly attaining an altogether different crystalline structure. On the practical side, the richness of possible phenomena renders the task of setting up numerical simulations particularly tricky  numerical artefacts, e.g. induced by prescribing a particular boundary condition, can lead to inconsistent results. In this talk I will aim to summarise ongoing efforts aimed at putting the atomistic modelling of fracture on a rigorous mathematical footing. I will introduce a framework giving rise to welldefined models for which regularity and stability of solutions can be discussed (topic of my PhD thesis at Warwick). I will then show how the theory can be used to set up practical simulations, such as Mode I fracture of silicon on the (111) cleavage plane using stateoftheart interatomic potentials. I will also outline how this framework can be used to rigorously derive upscaled models of nearcracktip plasticity. Finally, I will also talk about challenges in addressing the surface effects.

Geometry and Topology on 27 October 2022 at 14:00
Speaker: Daniel Berlyne (University of Bristol)
Title: Braid groups of graphs
Abstract: The braid group of a space X is the fundamental group of its configuration space, which tracks the motion of some number of particles as they travel through X. When X is a graph, the configuration space turns out to be a special cube complex, in the sense of Haglund and Wise. I show how these cube complexes are constructed and use graph of groups decompositions to provide methods for computing braid groups of various graphs, as well as criteria for a graph braid group to split as a free product. This has various applications, such as characterising various forms of hyperbolicity in graph braid groups and determining when a graph braid group is isomorphic to a rightangled Artin group.

Algebraic Geometry on 26 October 2022 at 15:00
Speaker: Arman Sarikyan (Edinburgh)
Title: On the Rationality of FanoEnriques Threefolds
Abstract: A threedimensional nonGorenstein Fano variety with at most canonical singularities is called a FanoEnriques threefold if it contains an ample Cartier divisor that is an Enriques surface with at most canonical singularities. There is no complete classification of FanoEnriques threefolds yet. However, L. Bayle has classified FanoEnriques threefolds with terminal cyclic quotient singularities in terms of their canonical coverings, which are smooth Fano threefolds in this case. The rationality of FanoEnriques threefolds is an open classical problem that goes back to the works of G. Fano and F. Enriques. In this talk we will discuss the rationality of FanoEnriques threefolds with terminal cyclic quotient singularities.

Postgraduate on 26 October 2022 at 12:00
Speaker: Robin Visser (University of Warwick)
Title: Hilbert's Tenth Problem
Abstract: Can you find four distinct positive integers $w,x,y,z$ such that $w^3+x^3=y^3+z^3$ ?
If that's too easy, try finding a nontrivial integer solution to $x^4+y^4+z^4=w^4$.
And good luck finding any integral solution to $x^3+y^3+z^3=114$.
This all begs the question of whether we can construct a general algorithm to determine whether any given Diophantine equation has integer solutions. David Hilbert posed this exact question at the second ICM in 1900, where a negative answer was finally proven 70 years later by Yuri Matiyasevich building on work by Martin Davis, Hilary Putnam and Julia Robinson. In this talk, we'll explore the mathematical ideas behind Hilbert's tenth problem as well as go over many surprising applications, extensions to other number fields, and how this relates to several other famous open problems! 
Algebraic Topology on 25 October 2022 at 16:00
Speaker: Severin Bunk (Oxford)
Title: Functorial field theories from differential cocycles
Abstract: In this talk I will demonstrate how differential cocycles give rise to (bordismtype) functorial field theories (FFTs). I will discuss some background on smooth FFTs, differential cohomology and higher gerbes with connection as a geometric model for differential cocycles before explaining the general principle for how to obtain smooth FFTs from higher gerbes. In the second part, I will focus on the twodimensional case. Here I will present a concrete, geometric construction of twodimensional smooth FFTs on background manifolds, starting from gerbes with connection. This is related to WZW theories. If time permits, I will comment on an extension of this construction which produces openclosed field theories.

Ergodic Theory and Dynamical Systems on 25 October 2022 at 14:00
Speaker: Maryam Hosseini (Open University)
Title: About Minimal Dynamics on the Cantor Set
Abstract: Dimension group is an operator algebraic object related to minimal dynamical systems on the Cantor set. In this talk after a quick review of some definitions of dimension group, the {\it topological and algebraic rank} of Cantor minimal systems are considered and we will see how the rank of a Cantor system is dominated by the rank of its extensions.

Partial Differential Equations and their Applications on 25 October 2022 at 12:00
Speaker: Alexandra Tzella (University of Birmingham)
Title: TBA
Abstract: TBA

Algebra on 24 October 2022 at 17:00
Speaker: Alexandre Zalesski (UEA)
Title: Some problems on representations of simple algebraic groups
Abstract: Some open questions on the weight structure of tensordecomposable representations of simple algebraic groups will be discussed.

Number Theory on 24 October 2022 at 15:00
Speaker: Aleksander Horawa (Oxford)
Title: Motivic action on coherent cohomology of Hilbert modular varieties
Abstract: A surprising property of the cohomology of locally symmetric spaces is that Hecke operators can act on multiple cohomological degrees with the same eigenvalues. We will discuss this phenomenon for the coherent cohomology of line bundles on modular curves and, more generally, Hilbert modular varieties. We propose an arithmetic explanation: a hidden degreeshifting action of a certain motivic cohomology group (the Stark unit group). This extends the conjectures of Venkatesh, Prasanna, and Harris to Hilbert modular varieties.

Colloquium on 21 October 2022 at 16:00
Speaker: Pierre Raphael (Cambridge)
Title: Singularity formation for super critical waves
Abstract: Give a wave packet an initial energy and let it propagate in the whole space, then in the linear regime, the wave packet will scatter. But in non linear regimes, part of the energy may concentrate to form coherent non linear structures which propagate without deformation (solitons). And in more extreme cases singularities may form. Whether or not singular structures arise is a delicate problem which has attracted a considerable amount of works in both mathematics and physics, in particular in the super critical regime which is the heart of the 6Th Clay problem on singularity formation for three dimensional viscous incompressible fluids. For another classical model like the defocusing Non Linear Schrodinger equation (NLS), Bourgain ruled out in a breakthrough work (1994) the existence of singularities in the critical case, and conjectured that this should extend to the super critical one. I will explain how the recent series of joint works with Merle (IHES), Rodnianski (Princeton) and Szeftel (Paris 6) shades a new light on super critical singularities: in fact there exist super critical singularities for (NLS), and the new underlying mechanism is directly connected to the first description of singularities for three dimensional viscous compressible fluids.

Combinatorics on 21 October 2022 at 14:00
Speaker: Daniel Iľkovič (Masaryk University)
Title: Quasirandom tournaments
Abstract: A directed graph H is quasirandomforcing for tournaments if the limit (homomorphic) density of H in a sequence of tournaments is 2^−E(H) if and only if the sequence is quasirandom. The cyclic orientation of a cycle of length k is quasirandomforcing if and only if k = 2 mod 4. We study a generalization of this result: what orientations of a cycle of length k are quasirandomforcing? We show that no orientation of an odd cycle is quasirandomforcing and classify which orientations of even cycles of length up to 10 are quasirandomforcing. This is joint work with Andrzej Grzesik, Bartosz Kielak and Dan Kráľ

Applied Mathematics on 21 October 2022 at 12:00
Speaker: Francis Aznaran (Oxford)
Title: Finite element methods for the Stokes–Onsager–Stefan–Maxwell equations of multicomponent flow
Abstract: The Onsager framework for linear irreversible thermodynamics provides a thermodynamically consistent model of mass transport in a phase consisting of multiple species, via the Stefan–Maxwell equations, but a complete description of the overall transport problem necessitates also solving the momentum equations for the flow velocity of the medium. We derive a novel nonlinear variational formulation of this coupling, called the (Navier–)Stokes–Onsager–Stefan–Maxwell system, which governs molecular diffusion and convection within a nonideal, singlephase fluid composed of multiple species, in the regime of low Reynolds number in the steady state. We propose an appropriate Picard linearisation posed in a novel Sobolev space relating to the diffusional driving forces, and prove convergence of a structurepreserving finite element discretisation. This represents some of the first rigorous numerics for the coupling of multicomponent molecular diffusion with compressible convective flow. The broad applicability of our theory is illustrated with simulations of the centrifugal separation of noble gases and the microfluidic mixing of hydrocarbons. This is joint work with Alexander VanBrunt.

Geometry and Topology on 20 October 2022 at 14:00
Speaker: Henry Bradford (Cambridge)
Title: TBA
Abstract: TBA

Algebraic Geometry on 19 October 2022 at 15:00
Speaker: Nivedita Viswanathan (Loughborough)
Title: On the Rationality of FanoEnriques Threefolds
Abstract: There has been a lot of development recently in understanding the existence of KahlerEinstein metrics on Fano manifolds due to the YauTianDonaldson conjecture, which gives us a way of looking at this problem in terms of the notion of Kstability. In particular, this problem is solved in totality for smooth del Pezzo surfaces by Tian. For del Pezzo surfaces with quotient singularities, there are partial results. In this talk, we will consider singular del Pezzo surfaces which are quasismooth, wellformed hypersurfaces in weighted projective space, and understand what we can say about their Kstability. This is ongoing joint work with InKyun Kim and Joonyeong Won.

Postgraduate on 19 October 2022 at 12:00
Speaker: Ruzhen Yang (University of Warwick)
Title: Beilinson spectral sequence and its reverse problems on PP^2
Abstract: Derived category is widely accepted as the natural environment to study homological algebra. We will study the structure of the bounded derived category of coherent sheaves on projective space via the semiorthogonal decomposition (based on the Beilinson's theorem) and comparison (by a theorem by A. Bondal). As an example, we will give explicit free resolutions of some sheaves on P2 using the Beilinson spectral sequence. We will also discuss the reverse problem where we give a condition to when the complex given by the spectral sequence is a resolution of the ideal sheaf of three points.

Algebraic Topology on 18 October 2022 at 16:00
Speaker: Thomas Read (Warwick)
Title: Gtypical Witt vectors with coefficients and the norm
Abstract: The norm is an important construction on equivariant spectra, most famously playing a key role in the work of Hill, Hopkins and Ravenel on the Kervaire invariant one problem. Witt vectors are an algebraic construction first used in Galois theory in the 1930s, but later finding applications in stable equivariant homotopy theory. I will describe a new generalisation of Witt vectors that can be used to compute the zeroth equivariant stable homotopy groups of the norm $N_e^G Z$, for $G$ a finite group and $Z$ a connective spectrum.

Ergodic Theory and Dynamical Systems on 18 October 2022 at 14:00
Speaker: Joe Thomas (Durham University)
Title: Poisson statistics, short geodesics and small eigenvalues on hyperbolic punctured spheres
Abstract: For hyperbolic surfaces, there is a deep connection between the geometry of closed geodesics and their spectral theoretic properties. In this talk, I will discuss recent work with Will Hide (Durham), where we study both sides of this relationship for hyperbolic punctured spheres. In particular, we consider WeilPetersson random surfaces and demonstrate Poisson statistics for counting functions of closed geodesics with lengths on scales 1/sqrt(number of cusps), in the large cusp regime. Using similar ideas, we show that typical hyperbolic punctured spheres with many cusps have lots of arbitrarily small eigenvalues. Throughout, I will contrast these findings to the setting of closed hyperbolic surfaces in the large genus regime.

Algebra on 17 October 2022 at 17:00
Speaker: Kamilla Rekvényi (Imperial College London)
Title: The Orbital Diameter of Primitive Permutation Groups
Abstract: Let G be a group acting transitively on a finite set Ω. Then G acts on ΩxΩ component wise. Define the orbitals to be the orbits of G on ΩxΩ. The diagonal orbital is the orbital of the form ∆ = {(α, α)α ∈ Ω}. The others are called nondiagonal orbitals. Let Γ be a nondiagonal orbital. Define an orbital graph to be the nondirected graph with vertex set Ω and edge set (α,β)∈ Γ with α,β∈ Ω. If the action of G on Ω is primitive, then all nondiagonal orbital graphs are connected. The orbital diameter of a primitive permutation group is the supremum of the diameters of its nondiagonal orbital graphs. There has been a lot of interest in finding bounds on the orbital diameter of primitive permutation groups. In my talk I will outline some important background information and the progress made towards finding explicit bounds on the orbital diameter. In particular, I will discuss some results on the orbital diameter of the groups of simple diagonal type and their connection to the covering number of finite simple groups. I will also discuss some results for affine groups, which provides a nice connection to the representation theory of quasisimple groups.

Number Theory on 17 October 2022 at 15:00
Speaker: Maria Rosaria Pati (Padova)
Title: Linvariants for cohomological representations of PGL(2) over an arbitrary number field
Abstract: In this talk I will construct the automorphic Linvariant attached to a cuspidal representation π of PGL(2) over an arbitrary number field F, and a prime p of F such that the local component πp is the Steinberg representation and π is noncritical at p. I will show that, if F is totally real then the automorphic Linvariant attached to π and p agrees with the derivatives of the Upeigenvalue of the padic family passing through π. From this I will deduce the equality between the automorphic Linvariant and the FontaineMazur Linvariant of the associated Galois representation. This is a joint work with Lennart Gehrmann.

Colloquium on 14 October 2022 at 16:00
Speaker: David Rand (Warwick)
Title: An appreciation of Christopher Zeeman
Abstract: In writing a biographical memoir of Zeeman for the Royal Society, I appreciated even more what a remarkable character he was, both in terms of his life, his leadership, his mathematics and his breadth of interests. I discovered a number of aspects that I don't think are very well known about his life and his contributions to topology, catastrophe theory and our department. In this colloquium I will try and give an overview of this.

Combinatorics on 14 October 2022 at 14:00
Speaker: Candy Bowtell (University of Warwick)
Title: The nqueens problem
Abstract: The nqueens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another, and the toroidal nqueens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of nqueens configurations on the classical board and T(n) the number of toroidal nqueens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture, prior to which no nontrivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{3})^n for all natural numbers n which was independently proved by Luria and Simkin and, combined with our toroidal result, completely settles a conjecture of Rivin, Vardi and Zimmerman regarding both Q(n) and T(n). In this talk we'll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4partite 4uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost' configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption. This is joint work with Peter Keevash.

Applied Mathematics on 14 October 2022 at 12:00
Speaker: Philip Herbert (HeriotWatt)
Title: Shape optimisation with Lipschitz functions
Abstract: In this talk, we discuss a novel method in PDE constrained shape optimisation. We begin by introducing the concept of PDE constrained shape optimisation. While it is known that many shape optimisation problems have a solution, their approximation in a meaningful way is nontrivial. To find a minimiser, it is typical to use first order methods. The novel method we propose is to deform the shape with fields which are a direction of steepest descent in the topology of W^1_\infty. We present an analysis of this in a discrete setting along with the existence of directions of steepest descent. Several numerical experiments will be considered which compare a classical Hilbertian approach to this novel approach.

Geometry and Topology on 13 October 2022 at 14:00
Speaker: Claudio Llosa Isenrich (KIT)
Title: Finiteness properties, subgroups of hyperbolic groups and complex hyperbolic lattices
Abstract: Hyperbolic groups form an important class of finitely generated groups that has attracted much attention in Geometric Group Theory. We call a group of finiteness type $F_n$ if it has a classifying space with finitely man cells of dimension at most n, generalising finite presentability, which is equivalent to type $F_2$. Hyperbolic groups are of type $F_n$ for all $n$ and it is natural to ask if their subgroups inherit these strong finiteness properties. We use methods from complex geometry to show that every uniform arithmetic lattice with positive first Betti number in $PU(n,1)$ admits a finite index subgroup, which maps onto the integers with kernel of type $F_{n1}$ and not $F_n$. This answers an old question of Brady and produces many finitely presented nonhyperbolic subgroups of hyperbolic groups. This is joint work with Pierre Py.

Algebraic Topology on 11 October 2022 at 16:00
Speaker: Sebastian Chenery (University of Southampton)
Title: On PushoutPullback Fibrations
Abstract: We will discuss recent work inspired by a paper of Jeffrey and Selick, where they ask whether the pullback bundle over a connected sum can itself be homeomorphic to a connected sum. We provide a framework to tackle this question through classical homotopy theory, before pivoting to rational homotopy theory to give an answer after taking based loop spaces.

Ergodic Theory and Dynamical Systems on 11 October 2022 at 14:00
Speaker: Sabrina Kombrink (University of Birmingham)
Title: TBA
Abstract: TBA

Algebra on 10 October 2022 at 17:00
Speaker: Gareth Tracey (University of Warwick)
Title: Primitive amalgams and the GoldschmidtSims conjecture
Abstract: The Classification of Finite Simple Groups has led to substantial progress on deriving sharp order bounds in various natural families of finite groups. One of the most wellknown instances of this is Sims' conjecture, which states that a point stabiliser in a primitive permutation group has order bounded in terms of its smallest nontrivial orbit length (this was proved by Cameron, Praeger, Saxl and Seitz using the CFSG in 1983). In the meantime, Goldschmidt observed that a generalised version of Sims' conjecture, which we now call the \emph{GoldschmidtSims conjecture}, would lead to important applications in graph theory. In this talk, we will describe the conjecture, and discuss some recent progress. Joint work with L. Pyber.

Number Theory on 10 October 2022 at 15:00
Speaker: Lambert A'Campo (Oxford)
Title: Galois representations and cohomology of congruence subgroups
Abstract: In this talk I will explain what it means to attach Galois representations to the cohomology of arithmetic locally symmetric spaces arising from congruence subgroups. In the case of GL(2) over imaginary CM fields (the method also works for GL(n)) I will explain how to prove, under certain conditions, that the Galois representations constructed by Harris–Lan–Taylor–Thorne and Scholze have good padic Hodge theoretic properties.

DAGGER on 10 October 2022 at 14:00
Speaker: Marco Linton (University of Oxford)
Title: Poison subgroups for hyperbolic groups
Abstract: It is a wellknown result that hyperbolic groups cannot contain certain `poison' subgroups. A lot of progress has been made towards understanding when the converse to this statement also holds. This includes several positive results, but also several negative results. In this talk, I will introduce hyperbolic groups, discuss some of these results and present the current state of the art for the class of onerelator groups.

Colloquium on 07 October 2022 at 16:00
Speaker: Michela Ottobre (HeriotWatt)
Title: Interacting Particle systems and (Stochastic) Partial Differential equations: modelling, analysis and computation
Abstract: The study of Interacting Particle Systems (IPSs) and related kinetic equations has attracted the interest of the mathematics and physics communities for decades. Such interest is kept alive by the continuous successes of this framework in modelling a vast range of phenomena, in diverse fields such as biology, social sciences, control engineering, economics, game theory, statistical sampling and simulation, neural networks etc. While such a large body of research has undoubtedly produced significant progress over the years, many important questions in this field remain open. We will (partially) survey some of the main research directions in this field and discuss open problems.

Combinatorics on 07 October 2022 at 14:00
Speaker: Mustazee Rahman (University of Durham)
Title: Suboptimality of local algorithms for optimization on sparse graphs
Abstract: Suppose we want to find the largest independent set or maximal cut in a large yet sparse graph, where the average vertex degree is constant. These are two basic optimization problems relevant to both theory and practice. For typical, or rather random sparse graphs, many algorithms proceed by way of local decision rules. Examples include Glauber dynamics, Belief propagation, etc. I will explain a form of local algorithm that captures many of these. I will then explain how they fail to find optimal independent sets or cuts once the average degree of the graph gets large. Along the way, we will find connections to entropy and spin glasses.

Geometry and Topology on 06 October 2022 at 14:00
Speaker: Grace Garden (University of Sydney)
Title: Earthquakes on the oncepunctured torus
Abstract: We study earthquake deformations on Teichmüller space associated with simple closed curves of the oncepunctured torus. We describe two methods to get an explicit form of the earthquake deformation for any simple closed curve. The first method is rooted in hyperbolic geometry, the second representation theory. The two methods align, providing both a geometric and an algebraic interpretation of the earthquake deformations. Pictures are given for earthquakes across multiple coordinate systems for Teichmüller space. Two families of curves are used as examples. Examining the limiting behaviour of each gives insight into earthquakes about measured geodesic laminations, of which simple closed curves are a special case.

Algebra on 05 October 2022 at 16:17
Speaker: Matija Vidmar (University of Ljubljana)
Title: Noise Boolean algebras: classicality, blackness and spectral independence
Abstract: Informally speaking, a noise Boolean algebra is an aggregate of pieces of information, subject to statistical independence properties relative to an underlying notion of chance. More formally, it is a distributive sublattice of the lattice of all subsigmafields of a given probability space, each element of which admits an independent complement. A noise Boolean algebra is classical (resp. black) when all its random variables are stable (resp. sensitive) under infinitesimal perturbations of its basic ingredients. For instance, the Wiener and Poisson noises are classical, but certain noises of percolation and coalescence are black. We shall see that classicality and blackness are respectively characterized by existence and nonexistence of certain socalled spectral independence probabilities that we shall introduce. Associated preprint: https://drive.google.com/file/d/1cLOHpHG_xgqPYmsbVIQmmYx08pqk4H6m/view

Postgraduate on 05 October 2022 at 12:00
Speaker: Sunny Sood (University of Warwick)
Title: Homological stability for $O_{n,n}$
Abstract: Motivated by Hermitian KTheory, we study the homological stability of the split orthogonal group $O_{n,n}$. Specifically, let $R$ be a commutative local ring with infinite residue field such that $2 \in R^{*}$. We prove that the natural homomorphism $H_{k}(O_{n,n}(R) ; \mathbb{Z}) \rightarrow H_{k}(O_{n+1,n+1}(R); \mathbb{Z})$ is an isomorphism for $k \leq n1$ and surjective for $k \leq n$. This will be an excellent opportunity to introduce esoteric concepts such as group homology and hyperhomology spectral sequences at the postgraduate seminar. This is all joint work with my supervisor Dr Marco Schlichting.

Partial Differential Equations and their Applications on 04 October 2022 at 12:00
Speaker: Tobias Barker (University of Bath)
Title: A quantitative approach to the Navier–Stokes equations
Abstract: ecently, Terence Tao used a new quantitative approach to infer that certain ‘slightly supercritical’ quantities for the Navier–Stokes equations must become unbounded near a potential blowup time. In this talk I’ll discuss a new strategy for proving quantitative bounds for the Navier–Stokes equations, as well as applications to behaviours of potentially singular solutions. This talk is based upon joint work with Christophe Prange (CNRS, Cergy Paris Université).

Number Theory on 03 October 2022 at 15:00
Speaker: Matteo Tamiozzo (Warwick)
Title: Perfectoid quaternionic Shimura varieties and the Jacquet–Langlands correspondence
Abstract: The Hodge–Tate period map can be thought of as a padic analogue of the Borel embedding. However, unlike its complex counterpart, it is not injective, and the pushforward of the constant sheaf via the Hodge–Tate period map encodes interesting arithmetic information. In the setting of quaternionic Shimura varieties, I will explain the relation between the structure of this complex of sheaves and level raising and the Jacquet–Langlands correspondence. I will then discuss applications to the study of the cohomology of quaternionic Shimura varieties. I will illustrate most of the arguments in the simplest setting of modular and Shimura curves. This is joint work with Ana Caraiani.

DAGGER on 03 October 2022 at 14:00
Speaker: Aleksi Pyörälä (University of Oulu)
Title: Normal numbers in selfconformal sets
Abstract: During recent years, the prevalence of normal numbers in natural subsets of the reals has been an active research topic in fractal geometry. The general idea is that in the absence of any special arithmetic structure, almost all numbers in a given set should be normal, in every base. In our recent joint work with Balázs Bárány, Antti Käenmäki and Meng Wu we verify this for selfconformal sets on the line. The result is a corollary of a uniform scaling property of selfconformal measures: roughly speaking, a measure is said to be uniformly scaling if the sequence of successive magnifications of the measure equidistributes, at almost every point, for a common distribution supported on the space of measures. Dynamical properties of these distributions often give information on the geometry of the uniformly scaling measure.